I was curious about the shape of ZE galaxies, that is, how the systems are arranged with respect to each other, which systems are close to each other, which are farther away.

Comparing the distances given for traveling from my home system in Galaxy 9 in the Standard Universe, it looks like the systems are arranged in a line in the same order as their system numbers. In other words, a long and very thin galaxy like this:

System 1 ---- System 2 ---- System 3 ---- ... ---- System 250

The distance between systems is a multiple of the difference between the system numbers.

I know that other universes have more systems per galaxy, but are all the galaxies in all the universes layed-out in the same way?

more or less, travel from one galaxy to another is fixed on the difference in the galaxy numbers as well.

In Extreme 499 systems in each galaxy

in massacre and speed 365.

I don't know about standard, you said 250?

Yes, the are laid out the same, progressively upwards. Standard where you are is basically the smallest server when it comes to numbers of systems. That being 250. That's why it's best to colonise near the centre of each galaxy. Standard, in or around system 125. That way at the start you have more scope for raiding, up and down the galaxy. Later when you have moons, gain sensor phalanxes, the need for a higher build level is not there, the maximum distance needed to scan systems would be 125 systems, cutting costs in your building.

(though by that logic if you want a planet/moon to hide at your best bet is a 1 or the highest available depending on the server to escape the people who cling to the middle)

Why do you need to escape those people? If you fleetsave, keep your stuff safe then it shouldn't be a problem, should it? Also, Standard has a maximum of 250 systems per galaxy, so nowhere is too far for anyone to go if you have colonised near the middle. I colonise at 125, a player goes and colonises system 1 or system 250. 125 systems away from me in the middle. Still close. Also, the more established players will have greater fleet speeds, nothing is more than 45-50 minutes away. If there is a target, nowhere would be safe. Unless you keep your stuff safe and fleetsave.